The number 47808
47808 is a composite number with 42 divisors. Its prime factorisation is × × 83. Divisors (42): 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72 … 47808.
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How to work it out
- 1
What is special about 47808: a happy number: repeatedly adding the squares of its digits reaches 1.
- 2
47808 is composite. Its prime factorisation is
- 3
The divisors add up to 138684; without 47808 itself that is 90876, so 47808 is abundant (90876 is more than 47808). Euler's totient φ(47808) = 15744 numbers up to 47808 share no factor with it.
- 4
The digits of 47808 add up to 27, and repeating that until one digit is left gives the digital root 9. The Collatz sequence (halve if even, else 3n+1) takes 52 steps to reach 1.
LaTeX source of the formulas on this page
\[ 47808 = 2^{6} \times 3^{2} \times 83 \]47808 at a glance
| Property | Value |
|---|---|
| Type | composite |
| Number of divisors | 42 |
| Sum of divisors | 138684 |
| Euler totient φ(n) | 15744 |
| Square | 2285604864 |
| Cube | 109270197338112 |
| Square root | 218.650406 (= 24√83) |
| Digit sum / digital root | 27 / 9 |
| Collatz steps to 1 | 52 |
| Scientific notation | 4.7808 × |
47808 in other forms
| Form | Value |
|---|---|
| In words | forty-seven thousand eight hundred and eight |
| Binary (base 2) | 1011101011000000 |
| Octal (base 8) | 135300 |
| Hexadecimal (base 16) | BAC0 |
| Base 3 | 2102120200 |
| As time | 47808 seconds = 13 h 16 min 48 s |
Is 47808 divisible by 2 to 12?
| Divisor | Answer | Rule |
|---|---|---|
| 2 | Yes (47808 ÷ 2 = 23904) | A number is divisible by 2 if the last digit is even (0, 2, 4, 6, 8). |
| 3 | Yes (47808 ÷ 3 = 15936) | A number is divisible by 3 if the digits add up to a multiple of 3. |
| 4 | Yes (47808 ÷ 4 = 11952) | A number is divisible by 4 if the last two digits make a multiple of 4. |
| 5 | No (remainder 3) | A number is divisible by 5 if the last digit is 0 or 5. |
| 6 | Yes (47808 ÷ 6 = 7968) | A number is divisible by 6 if it is divisible by both 2 and 3. |
| 7 | No (remainder 5) | A number is divisible by 7 if double the last digit and subtract it from the rest: the result is a multiple of 7. |
| 8 | Yes (47808 ÷ 8 = 5976) | A number is divisible by 8 if the last three digits make a multiple of 8. |
| 9 | Yes (47808 ÷ 9 = 5312) | A number is divisible by 9 if the digits add up to a multiple of 9. |
| 10 | No (remainder 8) | A number is divisible by 10 if the last digit is 0. |
| 11 | No (remainder 2) | A number is divisible by 11 if the alternating sum of the digits is a multiple of 11. |
| 12 | Yes (47808 ÷ 12 = 3984) | A number is divisible by 12 if it is divisible by both 3 and 4. |
Questions
Is 47808 a prime number?
No. 47808 = × × 83, so it is divisible by 2.
What are the factors of 47808?
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 64, 72, 83, 96, 144, 166, 192, 249, 288, 332, 498, 576, 664, 747, 996, 1328, 1494, 1992, 2656, 2988, 3984, 5312, 5976, 7968, 11952, 15936, 23904, 47808.
What is 47808 in binary?
1011101011000000 (hexadecimal BAC0, octal 135300).
What is the square root of 47808?
About 218.6504, exactly 24√83.
Is 47808 divisible by 3?
Yes. Its digits add up to 27, a multiple of 3.
What is special about the number 47808?
47808 is a happy number: repeatedly adding the squares of its digits reaches 1.